Lesson Worksheet: Binomial Theorem: Using Partial Fractions Mathematics
In this worksheet, we will practice decomposing rational expressions into partial fractions, then expanding them using the binomial theorem.
Q1:
By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.
- A,.
- B, .
- C, .
- D, .
- E, .
Q2:
By decomposing into partial fractions, find the cubic approximation of and state the range of values of for which the approximation is valid.
- A,
- B,
- C,
- D,
- E,
Q3:
By expressing in partial fractions, find the cubic expansion of and state the range of values of for which the approximation is valid.
- A,
- B,
- C,
- D,
- E,
Q4:
By expressing in partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.
- A,
- B,
- C,
- D,
- E,
Q5:
By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.
- A,
- B,
- C,
- D,
- E,
Q6:
By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.
- A,
- B,
- C,
- D,
- E,
Q7:
By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.
- A,
- B,
- C,
- D,
- E,
Q8:
By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.
- A,
- B,
- C,
- D,
- E,
Find the percentage error in using approximation to estimate the value of , giving your answer to 2 decimal places.
Q9:
By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.
- A,
- B,
- C,
- D,
- E,
Find the percentage error in using approximation to estimate the value of .
Q10:
By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.
- A,
- B,
- C,
- D,
- E,
Find the percentage error in using the approximation to estimate the value of , giving your answer to one decimal place.